Question

The radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find: (π = 3.14)

1. Curved surface area of frustum.
2. Total surface area of the frustum.
3. Volume of the frustum.

Answer 1

Given R = 14 cm, r = 8 cm and h = 8 cm

We need to calculate slant height.

l = `sqrt((R - r)^2 + h^2)`

= `sqrt((14 - 8)^2 + 8^2)`

= `sqrt((6)^2 + (8)^2)`

= `sqrt(36 + 64)`

= `sqrt(100)`

= 10 cm

i. Curved surface area of the frustum = π(R + r)l

= 3.14 × (14 + 8) × 10

= 3.14 × 22 × 10

= 3.14 × 220

= 690.8 cm²

ii. Total surface area of frustum = CSA + πR² + r²

= 690.8 + 3.14(R² + r²)

= 690.8 + 3.14(14² + 8²)

= 690.8 + 3.14(196 + 64)

= 690.8 + 615.44 + 200.96

= 1507.2 cm²

iii. Volume of the frustum = `1/3 pi h(R^2 + Rr + r^2)`

= `1/3 xx 3.14 xx 8 xx (14^2 + 14 xx 8 + 8^2)`

= `1/3 xx 3.14 xx 8 xx (196 + 112 + 64)`

= `1/3 xx 3.14 xx 8 xx (372)`

= `1/3 xx 3.14 xx 2976`

= `1/3 xx 9344.64`

= 3114.88 cm³